Worm gearing



, 1931. N; TRBOJEVICH July 21 WORM GEARING' Filed Aug. 6. 1928 2 Sheets-Sheet l July 21, 1931. N. T'RBOJEVQICH WORM GEARI NG Filed Aug. 6, 1928 2 Sheets-Sheet 2 As shown in Figure 2, the tools 13 move in a'tangential direction relative to the momentary root circle 16, from which it follows that the said tools will produce the maximum depth of cut at the instant when they pass through the midplane of the worrn. However, they will also remove metal both on circular. V-shaped ring surface 14, Figure 1 and will contact with the same at each instant along the two curves 17 and 18, Figure 2 respectively, one curve for each side of the thread. Said curves of momentary contact are known in mathematics as the characteristics of the generated surface and have theinteresting property that they lie both in'the'generating and the generated surface 7 in their entire lengths. Inasmuch as the generating. surface on one side of the worm thread is the convex faceof a clrcular cone, and onthe other side a concave face of another cone, it follows that the new thread surfaces are, entirely built up from a series of curves, all said curves having the common property in that they lie in a conical surface. The two curves 17 and 18, however, will not be alike or symmetrical and, furthermore,

"their lengths and curvatures will also continually change as the worm-11 is rotated and translated lengthwise as already stated.

vAs is seen in Figure l'the circular orbit 14 in which the generating tools aretranslated, is tangentto the thread helix at the point A in the midplane and interferes with the said helix at .the point G on approach and the point D on recess. As the interferences at (land D are not alike it follows that' the thread contours,-as measured in the midplane, will notbe symmetrical to each other with the consequence that the worm thread profiles as -measured in the midplane are of a variable contour. and are not alike at the driving and the coasting sides.

cutter relativeto the axis. of the worm is'best 7 Has seen in Figure 4. The cutter is adjusted so that the centerline of its cutting circle passes through the point A of the worm, and the center H of the said circle is offset relative to the axis 15in order to produce the desired helical angle G. g V T A worm gear adapted to mesh with the new globoid worm 11 is diagrammatically shown in Figures 5 and 6. The gear 21 has a plurality of circular teeth 22 formed about its circumference. It is to be noted that said teeth are not of a generated tooth form but are simply cut into the blank at spaced intervals by means of a circular cutter, the blank standing still during each such cut. As these teeth 22 are inclined at the desired helical angle relative to the gear axis 23 as indicated at J, Figure 5, it follows that they may be classified as curved hyperboloidal rack teeth and the gear in its outward appearance will resemble the gorge portion of a hyperboloid of revolution, i. e. it will be hollow in its midplane, as indicated at K, Figure 5. v l i Figure 7 shows on formation of a single tooth 22 of the gear 21. The body of said tooth is a segment of a V-shaped circular ring and may be swept by means of the tool 24: when said tool is moved in a circular path. I

The theory of this gearing requires that the curved tooth22, Figure 7 be of exactly the same curvature, thickness, etc. as thecutting path of the cutter 19,-Figure3. This may be accomplished by the'selection of two complementary cutters, one to cut the worm and the other the gear. As illustrated in Figure 8,

' the cutters 19 and 24 are'of exactly the same diameter and are complementary to each: other, i. e. when'superposed one over the other they will have a complete surface contact. From this we are in a position to show that] this method is theoretically correct,

i. e. that the finished worm and gear will mesh at a constant velocity and their corresponding teeth will always have a line contact with each other. The method of generating the worm, as already explained, is such that the thread surfaces arethe geometrical:

envelopes (of a single parameter) of the conical cutter surface and must therefore possess characteristics of aconicalcurve type. As the rotation and the. translation ofthe worm relative to the stationary cutter are 1 '35 anenlarged scale the timed according to a constant ratio,;it also follows that the principle of constant velocities is'properly taken care of. On the other hand, the wheel teeth all being the exact reproduction of the cutter and engaging the i 20 worm threads inexactly the same manner as the cutter does vduring the generation, will contact withrtheIworm' threads along the same above mentioned series of conical curves. 7

Figures 9 and 10 show a modification of the first described method of generating the worm 11. The cutter 25 having an axis 26 is no longer a Gleason cutter,'but is a conical cutter having its cutting. faces disposed in now away from the work thus rendering it possible to support the axis '15 by means of,

bearings of an ample length and diameter in order to insure the rigidity of the work support during generation. I

Figure 10 diagrammatically shows the formation of the modified worm cutter 25 from a given wheel cutter 24. 'The object is to produce as nearly as possible asurface contact to exist between the two comple I mentary cuttingv surfaces. While the, two

surfaces never can agree with a'theoreti'cal exactness, however, they may be fitted sufi'iciently close to each other so as to fall within the practical working tolerances, customary in this class of work. From the foregoing description, it will be evident that the new'process is adapted to grinding as well as toimilling operations.

hobbing. process in which case the. hob should be preferably of an hour-glass shape exactly corresponding in all its'principal dimensions to those of the mating worm. V The gear member of the drive may I be manufactured in an ordinary milling ma chine if form-cut as previously described, or V in an ordinary hobbing machine'if finished V by means of an hour-glass hob. -c The worm member may be generated in a special machine adapted to generate globoidal worms. A machine of that kind is illustrated and described in my copending application Serial No. 186,514, filed April'25, 1927. What I claim as "my invention is: v

1. A'w'orm rotatable about its axis com prising a body, a helical thread thereon so formed that its active surface is capable of contactingat any instant in a line-contact with a longitudinally'curved rack tooth having a'predetermined cross section and a tooth axis conforming with a predetermined plane curve, when the said rack tooth is being rotated'in a plane comprising the axis of the worm.

formed that its active surface is capable of contacting at any instant in, a line contact fandwadius when :the said rotated inja plane."

"3."globoidw'ornirotatable about'its axis the method for the purpose of a practical,

2. A worm rotatable about its axis comprising a body, av helical thread thereon s0 rack tooth is being comprising a bbdy, :a helicalthread so formed :tliatits Z'active'surface is "capable of contactingiatyan'y instant in acline ,contactywith a longitudinallyicui ved rack tooth having a predetermined cross section and a tooth axis conforming with a predetermined plane curve, when thesald-'raclr-tootl1- 1s bemgrotat'edfima plane; comprising the axis -of--;tlie worm in a circular orbit about a fixed center. i ejAgloboidwor'm rotatable-about its axis comprising faibody, a helical threadso formed that its'activesurface iscapableof contactingatvany instant in aline contact with a longitudinally curved circular rack tooth having a predetermined: cross section and radius when the saidracktooth is being rotated in a "plane comprisingthe 'axis'of the worm in a circularorbit abouta-fixed center. 5, Agloboid wormcomprising; a body "and athread formed thereon, said thread having two non-symmetrical flanks sjo formed that one flank is capable ofv engaging kin a line contact at 'every instant the convex sideof a predetermined longitudinally ,c11' rved'- circular rack tooth, andthe other fianlrcapable 10f similarly engaging the concave sideof the said rack tooth when the said toothqisbeingrotated in the axial plane of thesaidworm.

Also, the gear member of the drive may be manufactured by some other method than the one described such as, for instance, by the.

' 6. A globoid'worm, thethreadof whichhas two I non-symmetrical; flanks "sov formed-that oneflank is, capableof engaging in a line conabout a fixed center.

7; A- globoidf wjorm-- rotatable about its axis alif iiiompri's'ing' helical thread having two flanks, both of which are composed of a series of conical curves, said curves being arranged in such a manner that the worm will have a line contact with the teeth of a mating hyperboloidal wheel, said wheel having a plurality of equi-spaced longitudinally curved rack teeth conforming to a predetermined plane curve when the said wheel rotates about a fixed axis, at a fixed distance and atright angles with respect to the axis of the worm.

8. A globoid worm having its two active surfaces composed of two series of conical cular teeth, all the said teeth being inclined to their axis of rotation at the same helical angle.

9., A globoid wormhaving helical threads of a form such as might be generated by selecting a longitudinally curved circular rack tooth, in placing said tooth at an acute angle relative to the midplane, in aligning the curved axis of the tooth with the momentary tangent plane to the globoid surface, in rotating the Worm about its axis and in bodily translating thesa-id rack tooth in a timed relation in a circular orbit, in the said midplane and about a fixed axis perpendicular to the said midplane.

V 10; A pair of matingworm gears operat-. ing at a'fixed center distance and with their axes" disposed at right angles comprising a 'globoid worm and a mating Worm wheel, said Wheel comprising a plurality of longitudinally curved rack teeth equally spaced about the gorge portion of a hyperboloid of revolution in such a manner that the curves forming the axes of the teeth all'lie in planes tangent tothe said hyperboloid, and the angle of inclination of all teeth relative to the axis of r0- tation is the same; 7

' 11. A pair of mating Worm gears operating at a fixed center distance and with their axes disposed at right angles comprising a Worm having a thread which is Wound about the axis of rotation to conform with a'globoid helix of constant pitch and has two flanks composed of two series of conical curves, one

series being'copied from the convex side of a master cone and the other from the hollow side of another master cone, and a mating worm Wheel adapted to mesh with the said worm with a line contact at every instant.

12. A pair of matlng'worm gears comprlsing a globoid Worm and mating worm wheel adapted to mesh with each other With a line contact in which the teeth of the worm wheel are longitudinally curved and have two flanks for each tooth, one formedfrom the convex side of a cone and the other from the hollow side of another cone.

In testimony whereof I aflix my signature.

N IKOLA TRBOJEVICH. 

